What happens if the assassin fails to surprise their opponent but wins initiative?
He gets advantage until the target acts.
Do they get to use their assassinate power?
Yes, the part where they get advantage if they go before the target can act. No, they don't get to autocrit.
Did you think those questions were tricky, or something? I'm not understanding what you think my position is, because those would be clearly answerable if you did.
Ah, so you think that if the assassin wins initiative, he can autocrit when he autohits? Because I was under the impression that you thought that the conditions for surprise had to be met (usually a skill contest, but could be waived with DM fiat), then initiative must be rolled and won, and then the assassin had to hit his target successfully with a weapon attack before he got the benefit of the autocrit. Did you have a different sequence in mind? If so, what does the assassin have to do to get to the point where he autocrits?
Both parts of the assassinate ability require you to win initiative. The latter one occurs in an event when the former one would be redundant. You don't see that?
No, because it doesn't say that. It says that "any hit you score against a creature that is surprised is a critical hit." I suppose you could read that as also requiring that you beat their initiative, but you can also read it as just 'hitting a surprised creature -- however that occurs -- is a critical hit.
You ranked them. You said to use their primary archetype ability they need to win 3 checks. They don't, they only need to win initiative. Getting advantage on their attack is their primary archetype ability. People are ignoring it to argue that they are weaker in order to say that it is ridiculous that they only get to use their power when they surprise and win initiative.
I didn't rank them. Autocriting on surprise is part of the primary archetype ability. To use it, they need to win three checks.
Oh, wait. Are you saying that since the first part of the assassinate ability says something about initiative, that means that everything in the ability keys on initiative? Yeah, I don't get that at all.
And seriously, you still aren't agreeing about needing to win initiative? It's in the rules, in the sage advice, and Jeremy Crawford has tweeted about it multiple times explaining it to people.
Because the autocrit part doesn't say anything about initiative. It speaks only about surprise.
I don't know what else to say.
I don't know that you can say anything else. I've already agreed you have a strong position. I just disagree with it because I don't think it's fair to the assassin archetype for the reasons I've stated, and it isn't my bag anymore to run with blind RAW, "must follow the directives of the developer overlords to the detriment of my game," rulings anymore. Stretching surprise to last until the surprised creature takes an action doesn't break anything else, and allows assassinate to work more reliably for assassins. Given it's not a very strong ability, nor is it particularly powerful, that's an excellent solution that solves my issues with an initiative check acting as a second-chance perception check (or intuition check, or whatever). I see that you can make an good argument that that's how the rules work, but I don't like that outcome, so I can change it. The only place you'd ever notice that I had changed it would be if you were playing an assassin, so I find that a good solution because that's why I changed it.
So don't misunderstand my responses to you as attempting to change your mind or argue that I'm right. They're merely me explaining that I see your point, don't like it, and have decided to do something else.